Bijection classes for type \(A_{2n}^{(2)\dagger}\).

Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type \(A_{2n}^{(2)\dagger}\).

AUTHORS:

• Travis Scrimshaw (2012-12-21): Initial version

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(CartanType(['A', 4, 2]).dual(), [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import KRTToRCBijectionTypeA2Dual
sage: bijection = KRTToRCBijectionTypeA2Dual(KRT(pathlist=[[2,1]]))
sage: TestSuite(bijection).run()
sage: RC = RiggedConfigurations(CartanType(['A', 4, 2]).dual(), [[2, 1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import RCToKRTBijectionTypeA2Dual
sage: bijection = RCToKRTBijectionTypeA2Dual(RC(partition_list=[[],[]]))
sage: TestSuite(bijection).run()

class sage.combinat.rigged_configurations.bij_type_A2_dual.KRTToRCBijectionTypeA2Dual(tp_krt)

Bases: sage.combinat.rigged_configurations.bij_type_C.KRTToRCBijectionTypeC

Specific implementation of the bijection from KR tableaux to rigged configurations for type \(A_{2n}^{(2)\dagger}\).

This inherits from type \(C_n^{(1)}\) because we use the same methods in some places.

next_state(val)

Build the next state for type \(A_{2n}^{(2)\dagger}\).

TESTS:

sage: KRT = crystals.TensorProductOfKirillovReshetikhinTableaux(CartanType(['A', 4, 2]).dual(), [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import KRTToRCBijectionTypeA2Dual
sage: bijection = KRTToRCBijectionTypeA2Dual(KRT(pathlist=[[-1,2]]))
sage: bijection.cur_path.insert(0, [])
sage: bijection.cur_dims.insert(0, [0, 1])
sage: bijection.cur_path[0].insert(0, [2])
sage: bijection.next_state(2)

class sage.combinat.rigged_configurations.bij_type_A2_dual.RCToKRTBijectionTypeA2Dual(RC_element)

Bases: sage.combinat.rigged_configurations.bij_type_C.RCToKRTBijectionTypeC

Specific implementation of the bijection from rigged configurations to tensor products of KR tableaux for type \(A_{2n}^{(2)\dagger}\).

next_state(height)

Build the next state for type \(A_{2n}^{(2)\dagger}\).

TESTS:

sage: RC = RiggedConfigurations(CartanType(['A', 4, 2]).dual(), [[2,1]])
sage: from sage.combinat.rigged_configurations.bij_type_A2_dual import RCToKRTBijectionTypeA2Dual
sage: bijection = RCToKRTBijectionTypeA2Dual(RC(partition_list=[[2],[2,2]]))
sage: bijection.next_state(1)
-1